2020/11/01 by Tarik Dzanic, Will Trojak, Dzanic, Tarik +4
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Classification of discontinuities #Computational Fluid Dynamics and Aerodynamics #Discontinuity (linguistics) #Discontinuous Galerkin method #Dissipation #Euler equations #FOS: Mathematics #Finite element method #Finite volume method #Fluid Dynamics and Turbulent Flows #Generalization #Invariant (physics) #Mathematical analysis #Mathematics #Mechanics #Nonlinear system #Numerical Analysis (math.NA) #Numerical methods for differential equations #Physics #Riemann hypothesis #Riemann problem #Riemann solver #Spurious relationship #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2011.06418
16 pages, 8 figures
arxiv created 2020/11/01 · openalex publication_date 2020/11/01 · arxiv updated 2020/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a novel structure-preserving numerical scheme for discontinuous finite element approximations of nonlinear hyperbolic systems. The method can be understood as a generalization of the Lax-Friedrichs flux to a high-order staggered grid and does not depend on any tunable parameters. Under a presented set of conditions, we show that the method is conservative and invariant domain preserving. Numerical experiments on the Euler equations show the ability of the scheme to resolve discontinuities without introducing excessive spurious oscillations or dissipation.